Our intuition shapes the models we use to describe nature. Across centuries, light has long been described as rays, tiny particles or electromagnetic waves. However, the quantum world is now challenging this view: light can be described in any of these ways, but is neither of them. The same is true for particles of matter: electrons, protons and neutrons behave like waves and produce interference patterns. Today, these bizarre phenomena are at the core of emerging technologies with an enormous potential.